A field, F, is called C_r if every homogenous form of degree n in more then n^r variables has a non-trivial solution.

Consider a central simple algebra, A, of exponent n over a field F. By the Merkurjev-Suslin theorem assuming F contains a primitive n-th root of one, A is similar to the product of symbol algebras, the smallest number of symbols required is called the length of A denoted l(A).

If F is C_r we prove l(A) \leq n^{r-}-1. In particular the length is independent of the index of A.